Introduction to Matrices - Online Tutor, Practice Problems & Exam Prep

Consider the following matrices and perform the indicated operation:

C(AB)

Consider the following matrices and perform the indicated operation:

A + B

Consider the following matrices and perform the indicated operation:

AB - BA

Consider the following matrices and perform the indicated operation:

2A - 4B  

Perform the following matrix operation: 2A - 5B

Perform the following matrix operation: 9A

Perform the following matrix operation: A - B

Perform the following matrix operation: A + B

Perform the following matrix operation: - A + 4B

Perform the following matrix operation: - 5D

Perform the following matrix operation: A - B

Perform the following matrix operation: A + B

Consider the following matrices:

Solve the following matrix equation for X: 6A + 2B = - 3X

Perform the following matrix operation: - 2A + 4B

Consider the following matrices:

Solve the following matrix equation for X: 2B - X = 5A

Perform the following matrix operation: 5B

Perform the following matrix operation: A - B

Perform the following matrix operation: A + B

Consider the following matrices:

Solve the following matrix equation for X: 2X + 4A = B

Consider the following matrices:

Solve the following matrix equation for X: 4X - A = B

Consider the following matrices:

Solve the following matrix equation for X: X + A = B

Perform the following matrix operation: - 2A

Perform the following matrix operation: A - B

Perform the following matrix operation: A + B

Perform the following matrix operation: - 2A + 5B

Perform the following matrix operation: - 3A

Perform the following matrix operation: A - B

Perform the following matrix operation: A + B

Perform the following matrix operation: 5A - 3B

Perform the following matrix operation: - 9A

Perform the following matrix operation: A - B

Perform the following matrix operation: A + B

Find the given matrices (if possible):
a. PQ
b. QP

Find the given matrices (if possible):
a. PQ
b. QP

Find the given matrices (if possible):
a. PQ
b. QP

Find the given matrices (if possible):
a. PQ
b. QP

Find the given matrices (if possible):
a. PQ
b. QP

To make the matrices in the question equal, determine values for the variables.

To make the matrices in the question equal, determine values for the variables.

If A = [a_ij], find a₁₄ and a₃₁ and state the matrix's order. If identification is not possible, state why.

If A = [a_ij], find a₁₃ and a₃₁ and state the matrix's order. If identification is not possible, state why.

Determine the augmented matrix that corresponds to the system of equations shown:

Write a new matrix after applying mentioned row operations 

Find the number of rows and columns in the following matrix. Also, find the dimension of the matrix.

Determine the augmented matrix that corresponds to the system of equations shown:

Using Gaussian elimination or Gauss-Jordan elimination, provide a solution for the following system of equations using matrices. 

Write the augmented matrix for the system of linear equations given below.

Using Gaussian elimination or Gauss-Jordan elimination, provide a solution for the following system of equations using matrices. 

By using Gaussian elimination or Gauss-Jordan elimination, provide a solution for the following system of equations using matrices. 

Determine the augmented matrix that corresponds to the system of equations shown:

Apply the indicated row transformation to the following matrix.

Add the result -5 times of row 1 to row 2

Determine the augmented matrix that corresponds to the system of equations shown:

Apply the indicated row transformation to the following matrix.

Add the result -10 times of row 1 to row 2

Determine the system of linear equations associated to the following augmented matrix. Use the variables x, y, and z.

Apply the indicated row transformation to the following matrix.

Add the result 6 times of row 1 to row 2

Apply the indicated row transformation to the following matrix.

Add the result 8 times of row 1 to row 2

Determine the system of linear equations associated to the following augmented matrix. Use the variables w, x, y, and z.

What is the augmented matrix for the following system of equations? Also, state the dimension of the matrix. Please note that you don't need to solve it.

Write the new matrix after performing the matrix row operation.

What is the augmented matrix for the following system of equations? Also, state the dimension of the matrix. Please note that you don't need to solve it.

Consider these given matrices A and B, and perform the mentioned matrix operation. Also, state the reason if the operation is not defined. 

Write the new matrix after performing the matrix row operation.

What is the system of equations associated with the following augmented matrix? Please note that you don't need to solve it.

Consider these given matrices P and Q, and perform the mentioned matrix operation. Also, state the reason if the operation is not defined. 

Write the new matrix after performing the matrix row operation.

What is the system of equations associated with the following augmented matrix? Please note that you don't need to solve it.

Consider these given matrices P and Q, and perform the mentioned matrix operation. Also, state the reason if the operation is not defined. 

Follow the procedures and fill in the missing numbers where, in the process of reducing the provided matrix to row-echelon form, with 1s running diagonally from upper left to lower right and 0s below the 1s, is demonstrated in a few steps. 

What is the system of equations associated with the following augmented matrix? Please note that you don't need to solve it.

Consider these given matrices P and Q, and perform the mentioned matrix operation. Also, state the reason if the operation is not defined. 

Solve the system of equations using the Gauss-Jordan method and provide the solution with y arbitrary for systems in two variables that have infinitely many solutions. 

Using Gaussian elimination with back-substitution or Gauss-Jordan elimination, solve the given system of equations. 

Solve the system of equations using the Gauss-Jordan method and provide the solution with y arbitrary for systems in two variables that have infinitely many solutions. 

Using Gaussian elimination with back-substitution or Gauss-Jordan elimination, solve the given system of equations. 

Consider these given matrices P and Q, and perform the mentioned matrix operation. Also, state the reason if the operation is not defined. 

Solve the given system of linear equations using the Gauss-Jordan method.

3x + y = -12

x - 2y = -4

Using Gaussian elimination with back-substitution or Gauss-Jordan elimination, solve the given system of equations. 

Solve the system of equations using the Gauss-Jordan method and provide the solution with y arbitrary for systems in two variables that have infinitely many solutions. 

Using Gaussian elimination with back-substitution or Gauss-Jordan elimination, solve the given system of equations. 

Solve the system of equations using the Gauss-Jordan method and provide the solution with y arbitrary for systems in two variables that have infinitely many solutions. 

Solve the given system of linear equations using the Gaussian elimination method.

2x - y = 2

x - y = 3

In the given matrix equation, find X. Provided,

Solve the system of equations using the Gauss-Jordan method and provide the solution with y arbitrary for systems in two variables that have infinitely many solutions. 

Solve the given system of linear equations using the Gauss-Jordan method.

x - z = -1

y + z = 4

4x - 5z = -7

Using Gaussian elimination with back-substitution or Gauss-Jordan elimination, solve the given system of equations. 

Solve the given system of equations using the Gauss-Jordan method, and if the system has infinitely many solutions, express the solution set with z being arbitrary.

Using Gaussian elimination with back-substitution or Gauss-Jordan elimination, solve the given system of equations. 

Using Gaussian elimination with back-substitution or Gauss-Jordan elimination, solve the given system of equations. 

Using Gaussian elimination with back-substitution or Gauss-Jordan elimination, solve the given system of equations. 

Using Gaussian elimination with back-substitution or Gauss-Jordan elimination, solve the given system of equations.

If ƒ(2) = -3, ƒ(1) = 2, and ƒ(-1) = 0, identify the quadratic function f(x) = ax² + bx + c.

If ƒ(1) = -7, ƒ(-1) = -15, ƒ(2) = 0, and ƒ(-2) = -52, identify the cubic function ƒ(x) = ax³ + bx² + cx + d.

Solve the system of equations given below.

Find the solution using the elimination method. 

Solve the given three-variable equation system:

Solve the given three-variable equation system:

Work out the values of A, B, and C.

A + B = 2
5A + 8B - C = 1
6A - 3C = 0

If a quadratic function's (y = ax² + bx + c) graph passes through the given points (-1, 7), (1, 11), and (-2, 29), find the quadratic function.

If a quadratic function's (y = ax² + bx + c) graph passes through the given points (2, 3), (-1, 1), and (1, 2), find the quadratic function.

Solve the three-variable equation system:

Solve the three-variable equation system:

Solve the three-variable equation system:

Solve the three-variable equation system:

Solve the three-variable equation system:

Solve the three-variable equation system:

Solve the three-variable equation system: 

Find out whether the given ordered triple satisfies the system of equations shown. 

(3, 1, 7) 

Find out whether the given ordered triple satisfies the system of equations shown.
(1, −1, 2) 

Determine the coefficient of x², x and the constant R in the given function y = Px²+Qx+R, which passes through (-3, 0), (0, 3), and (1, 0)

Solve the given system of equation 

x + y + z = 3

3x + y - 2z = 6

x -2y - z = 3

In a triangle ABC, the measure of the smallest angle is 20° less than the measure of the medium angle and the measure of the largest angle is 50° less than thrice the measure of the medium angle. Find all three angles of the triangle.

Solve the given system of linear equations.

Determine the quantity of each type of ball purchased by a sports teacher who bought a total of 40 balls. The number of basketballs exceeds the number of footballs by 8. Given that the cost of a tennis ball is $4, a basketball is $5, and a football is $7, the total cost of the purchase was $184.

The manufacturer of cement plans to produce 500 kg of cement and sell it for $5.00 per kg. She intends to mix three grades of cement with different prices - $10.00, $8.00, and $4.00 per kg. She must use three times more of the $4.00 cement than the $8.00 cement. What amount of each grade should she mix?

For the following expression, (7x² + 6x + 23)/(x³ - 18x - 35), perform partial fraction decomposition.

For the following expression, 3/[y(y + 3)], perform partial fraction decomposition, and using the resulting expression, evaluate the following addition:

Using long division, work out the following expression and expand its remainder by doing partial fraction decomposition. 

(s⁴ - 16s² + 8)/(s³ - 4s²)

Using long division, work out the following expression and expand its remainder by doing partial fraction decomposition. 

(y⁵ + 3)/(y² - 9)

Express the following expression in its partial fraction decomposition.

(3c² - 10c + 50)/(c³ - 125)

Express the following expression in its partial fraction decomposition.

(y³ - 11y² + 36y - 31)/(y² - 4y + 5)²

Express the following expression in its partial fraction decomposition.

(y³ + 2y² + y + 12)/(y² + 6)²

Express the following expression in its partial fraction decomposition.

(4x² + 2x - 18)/[(x + 3)(x² + 3)]

Express the following expression in its partial fraction decomposition.

(9y + 1)/[y²(y² + 9)]

Express the following expression in its partial fraction decomposition.

(6y² - 3y + 45)/[(y - 5)(y² + 3y + 5)]

Express the following expression in its partial fraction decomposition.

(9a² - 10a + 57)/(a - 3)(a² + 9)

Express the following expression in its partial fraction decomposition.

4y²/[(y - 2)²(y + 2)]

Express the following expression in its partial fraction decomposition.

(- 2a² + 13a + 36)/[a(a - 6)²]

Express the following expression in its partial fraction decomposition.

(2d² - 23d + 58)/(d - 5)³

Express the following expression in its partial fraction decomposition.

(2d - 13)/(d - 9)²

Express the following expression in its partial fraction decomposition.

(2b² - b - 6)/(b³ - 36b)

Express the following expression in its partial fraction decomposition.

(3a² - 2a - 9)/(a³ - 9a)

Express the following expression in its partial fraction decomposition.

(2y² + 5y - 4)/[y(y - 2)(y + 5)]

Express the following expression in its partial fraction decomposition.

8y/(y² + 4y - 12)

Express the following expression in its partial fraction decomposition.

7/(3y² - y - 4)

Express the following expression in its partial fraction decomposition.

(4y + 16)/(y² + 4y - 12)

Express the following expression in its partial fraction decomposition.

(2y - 9)/(y² - 2y - 35)

Express the following expression in its partial fraction decomposition.

(5x + 19)/(x - 1)(x + 3)

Express the following expression in its partial fraction decomposition.

14/y(y - 7)

Express the following expression in its partial fraction decomposition.

y/(y - 4)(y - 8)

Rewrite the following expression in the partial fraction decomposition form. Do not solve for the constants!

(3x² - 13x + 25)/(x² + 11)² 

Rewrite the following expression in the partial fraction decomposition form. Do not solve for the constants!

(3x³ + 2x²)/(x² + 9)² 

Rewrite the following expression in the partial fraction decomposition form. Do not solve for the constants!

(7x² - 9x + 13)/(x - 4)(x² + 4)

Rewrite the following expression in the partial fraction decomposition form. Do not solve for the constants!

(8y + 9)/(y + 3)(y - 5)²

Rewrite the following expression in the partial fraction decomposition form. Do not solve for the constants!

(8x² - 39x - 163)/(x + 4)(x - 7)²

Rewrite the following expression in the partial fraction decomposition form. Do not solve for the constants!

(2x - 98)/(x - 9)(x + 5)

Find the sum: (2x - 1)/(x² + 9) + 5x/(x² + 9)²

Find the difference: 8/(x - 3) - 5/(x + 6)

For the given rational expression, write in its partial fraction decomposition form.

(2x³ - 4x² - 3x + 1)/(x² + 2x + 3)²

For the given rational expression, write in its partial fraction decomposition form.

(x² + 2x - 10)/(x + 2)(x² + 1)

For the given rational expression, write in its partial fraction decomposition form.

2x/(x + 2)(x² + 4)

For the given rational expression, write in its partial fraction decomposition form.

(x² - 2x + 1)/x(x + 1)(x - 1)

For the given rational expression, write in its partial fraction decomposition form.

x/(x + 5)(x - 4)

What should be multiplied to each side of 9/[7p(5p + 11)] = x/7p + y/(5p + 11), so that the fraction form of the equation is removed? 

What should be multiplied to each side of (8z -1)/(z + 5)(2z² + 7) = A/(z + 5) + (Bz + C)/(2z² + 7), so that the fraction form of the equation is removed? 

What should be multiplied by each side of (5y - 3)/y(9y² + 2)² = A/y + (By + C)/(9y² + 2) + (Dy + E)/(9y² + 2)², so that the fraction form of the equation is removed? 

For the following rational expression, apply partial fraction decomposition.

8/(5P(7P +3))

For the following rational expression, apply partial fraction decomposition.

(8p +4)/((p + 2)(5p -6))

For the following rational expression, apply partial fraction decomposition.

p/(p² -4p -21)

Decompose the given rational function in partial fractions. 

17/t(t +1)

Decompose the given rational function in partial fractions. 

(3p² +4p +28)/[p(p +2)(p -2)]

Decompose the given rational function in partial fractions. 

(3t +2)/(t +5)³

For the following rational expression, apply partial fraction decomposition. 

(t²)/(t² + 6t +9)

For the following rational expression, apply partial fraction decomposition. 

(t³ +7)/(4t³ -t)

For the following rational expression, apply partial fraction decomposition.

-9/[t²(t² +7)]

For the following rational expression, apply partial fraction decomposition.

(5t - 2)/((t +1)(3t² +3))

For the following rational expression, apply partial fraction decomposition.

1/t(4t +1)(2t² +1)

For the following rational expression, apply partial fraction decomposition. 

(3x⁵-19x⁴+37x³-21x²+x+1)/(3x²-16x+21)

Decompose the given rational function in partial fractions. 

(6t -7)/t(3t² +2)²

Decompose the given rational function in partial fractions. 

(-7x⁴-28x²+5x+7)/(x + 7)(x² +2)²

Decompose the given rational function in partial fractions. 

(3t²)/7(t⁴ - 1)

Decompose the given rational function in partial fractions. 

(3t²-t+3)/(t³-2t²-3t)

For the following rational expression, apply partial fraction decomposition.

(7 -3x)/[(x² +7)(x -3)]

Find the complete solution or indicate that there is none for this given system of equations using Gaussian Elimination.

Find the complete solution or indicate that there is none for this given system of equations using Gaussian Elimination.

Find the complete solution or indicate that there is none for this given system of equations using Gaussian Elimination.

Find the complete solution or indicate that there is none for this given system of equations using Gaussian Elimination.

Find the complete solution or indicate that there is none for this given system of equations using Gaussian Elimination.

Find the complete solution or indicate that there is none for this given system of equations using Gaussian Elimination.

Find the complete solution or indicate that there is none for this given system of equations using Gaussian Elimination.

Find the complete solution or indicate that there is none for this given system of equations using Gaussian Elimination.

Find the complete solution or indicate that there is none for this given system of equations using Gaussian Elimination.

Find the complete solution or indicate that there is none for this given system of equations using Gaussian Elimination.

Find the complete solution or indicate that there is none for this given system of equations using Gaussian Elimination.

Find the complete solution or indicate that there is none for this given system of equations using Gaussian Elimination.

For the following system of equations, use the Gaussian elimination method to determine the solution or to identify if no solution exists:

For the following system of equations, use the Gaussian elimination method to determine the solution or to identify if no solution exists:

For the following system of equations, use the Gaussian elimination method to determine the solution or to identify if no solution exists: